where \(l=1,2\)  are labels of the bottom and top layers respectively. \(H_{\mathrm {int}}\)  describes the van der Waals interaction between two layers
[1]}, [2]}, [3]}. The meanings of various interlayer couplings \(\gamma _{i} \)  with \(i=1,3,4\)  are indicated in Fig. REF . \(H_{\mathrm {on-site}}\)  is the on-site potentials of the system such as interlayer bias \(U\)  as
shown in Fig. REF . Here, we take \(t=3.16\mathrm {eV}\) , \(\gamma _{1}=0.381\mathrm {eV}\)  as typical experimental values for AB-stacked BLGs
[4]}, and \(\gamma _{4}=0\)  throughout this work since it is pretty
small compared with others in realistic systems [1]}, [3]}, [4]}. We
choose \(\gamma _{3}=0.38\mathrm {eV}\approx \gamma _{1}\)  when considering the
non-zero \(\gamma _{3}\) , which is close to most of the experimental
observations [1]}, [3]}, [4]}\(.\)
<FIGURE>